In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct quasi elastic limit providing a consistent spectral method for the limiting nonlinear friction equation.
Mots-clés : Boltzmann equation, granular media, spectral methods, singular integrals, nonlinear friction equation, quasi elastic limit
@article{M2AN_2003__37_1_73_0,
author = {Naldi, Giovanni and Pareschi, Lorenzo and Toscani, Giuseppe},
title = {Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {73--90},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003019},
mrnumber = {1972651},
zbl = {1046.76034},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003019/}
}
TY - JOUR AU - Naldi, Giovanni AU - Pareschi, Lorenzo AU - Toscani, Giuseppe TI - Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 73 EP - 90 VL - 37 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003019/ DO - 10.1051/m2an:2003019 LA - en ID - M2AN_2003__37_1_73_0 ER -
%0 Journal Article %A Naldi, Giovanni %A Pareschi, Lorenzo %A Toscani, Giuseppe %T Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 73-90 %V 37 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003019/ %R 10.1051/m2an:2003019 %G en %F M2AN_2003__37_1_73_0
Naldi, Giovanni; Pareschi, Lorenzo; Toscani, Giuseppe. Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 73-90. doi : 10.1051/m2an:2003019. http://www.numdam.org/articles/10.1051/m2an:2003019/
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